The drying times of a certain type of new paint are known to follow normal distribution with mean µ == 75 mins and standard deviation o = 9 mins. Chemists have proposed a net additive to shorten the drying time. It is believed that with this new addition, the dryin, times are still normally distributed with the same variance but with a smaller mean parameter H. One is therefore interested in testing Ho u = 75 versus H : u < 75. Experts in the area decide that a value for u smaller than 70 indicates a practically useful improvement, therefore a rejection region for Ho in favor of H is taken to be {X < 70}, where X is the sample mean based on a random sample of size n from the paint with this new addition. (a) Calculate and interpret the probability of type 1 error. (b) Calculate and interpret the probability of type 2 error when the true u = 68. (c) What's the smallest sample size n such that this test procedure (reject Ho when X < 70) has only 10% probability of type 2 error when the true u = 68? (d) Determine the test procedure that has a fixed probability of type 1 error equal to a ..izo

The drying times of a certain type of new paint are known to follow normal distribution with mean µ == 75 mins and standard deviation o = 9 mins. Chemists have proposed a net additive to shorten the drying time. It is believed that with this new addition, the dryin, times are still normally distributed with the same variance but with a smaller mean parameter H. One is therefore interested in testing Ho u = 75 versus H : u < 75. Experts in the area decide that a value for u smaller than 70 indicates a practically useful improvement, therefore a rejection region for Ho in favor of H is taken to be {X < 70}, where X is the sample mean based on a random sample of size n from the paint with this new addition. (a) Calculate and interpret the probability of type 1 error. (b) Calculate and interpret the probability of type 2 error when the true u = 68. (c) What's the smallest sample size n such that this test procedure (reject Ho when X < 70) has only 10% probability of type 2 error when the true u = 68? (d) Determine the test procedure that has a fixed probability of type 1 error equal to a ..izo

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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